{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T18:40:34Z","timestamp":1791916834776,"version":"4.3.4"},"reference-count":21,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","funder":[{"DOI":"10.13039\/501100001711","name":"SNSF","doi-asserted-by":"crossref","award":["192363"],"award-info":[{"award-number":["192363"]}],"id":[{"id":"10.13039\/501100001711","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Sci. Comput."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>Tensor trains are a versatile tool to compress and work with high-dimensional data and functions. In this work we introduce the streaming tensor train approximation (STTA), a new class of algorithms for approximating a given tensor [Formula: see text] in the tensor train format. STTA accesses [Formula: see text] exclusively via two-sided random sketches of the original data, making it streamable and easy to implement in parallel\u2014unlike existing deterministic and randomized tensor train approximations. This property also allows STTA to conveniently leverage structures in [Formula: see text], such as sparsity and various low-rank tensor formats, as well as linear combinations thereof. When Gaussian random matrices are used for sketching, STTA is admissible for an analysis that builds and extends upon existing results on the generalized Nystr\u00f6m approximation for matrices. Our results show that STTA can be expected to attain a nearly optimal approximation error if the sizes of the sketches are suitably chosen. A range of numerical experiments illustrates the performance of STTA compared to existing deterministic and randomized approaches.<\/jats:p>","DOI":"10.1137\/22m1515045","type":"journal-article","created":{"date-parts":[[2023,10,4]],"date-time":"2023-10-04T04:13:51Z","timestamp":1696392831000},"page":"A2610-A2631","source":"Crossref","is-referenced-by-count":22,"title":["Streaming Tensor Train Approximation"],"prefix":"10.1137","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3369-2958","authenticated-orcid":true,"given":"Daniel","family":"Kressner","sequence":"first","affiliation":[{"name":"Institute of Mathematics, EPFL, CH-1015 Lausanne, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6501-816X","authenticated-orcid":true,"given":"Bart","family":"Vandereycken","sequence":"additional","affiliation":[{"name":"Section of Mathematics, University of Geneva, CH-1205 Geneva, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7824-9269","authenticated-orcid":true,"given":"Rik","family":"Voorhaar","sequence":"additional","affiliation":[{"name":"Section of Mathematics, University of Geneva, CH-1205 Geneva, Switzerland."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2023,10,4]]},"reference":[{"key":"ref1","unstructured":"D. Aksoy , \nD. J. Gorsich , \nS. Veerapaneni , and \nA. A. Gorodetsky  , An Incremental Tensor Train Decomposition Algorithm, preprint, https:\/\/doi.org\/10.48550\/arXiv.2211.12487, 2022."},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/21M1451191"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1137\/20M131936X"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-016-9317-9"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-018-9622-8"},{"key":"ref6","doi-asserted-by":"crossref","unstructured":"K. L. Clarkson  and \nD. P. Woodruff  , Numerical linear algebra in the streaming model, in Proceedings of the Forty-First Annual ACM Symposium on Theory of Computing, Association for Computing Machinery, New York, 2009, pp. 205\u2013214, https:\/\/doi.org\/10.1145\/1536414.1536445.","DOI":"10.1145\/1536414.1536445"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1002\/gamm.201310004"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-35554-8"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1137\/090771806"},{"key":"ref10","doi-asserted-by":"crossref","unstructured":"B. Huber , \nR. Schneider , and \nS. Wolf  , A randomized tensor train singular value decomposition, in Compressed Sensing and Its Applications: Second International MATHEON Conference 2015, Appl. Numer. Harmon. 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Nakatsukasa  , Fast and Stable Randomized Low-Rank Matrix Approximation, preprint, arXiv:2009.11392, 2020, https:\/\/doi.org\/10.48550\/arXiv.2009.11392."},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1016\/j.aop.2014.06.013"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1137\/090752286"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.aop.2010.09.012"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1137\/21M146079X"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1137\/17M1111590"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-31351-7_9"},{"key":"ref21","unstructured":"S. Wolf  , Low Rank Tensor Decompositions for High Dimensional Data Approximation, Recovery and Prediction, Ph.D. thesis, TU Berlin, Berlin, 2019, https:\/\/doi.org\/10.14279\/depositonce-8109."}],"container-title":["SIAM Journal on Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/22M1515045","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:46:41Z","timestamp":1787327201000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/22M1515045"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,4]]},"references-count":21,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2023,10,31]]}},"alternative-id":["10.1137\/22M1515045"],"URL":"https:\/\/doi.org\/10.1137\/22m1515045","relation":{},"ISSN":["1064-8275","1095-7197"],"issn-type":[{"value":"1064-8275","type":"print"},{"value":"1095-7197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,10,4]]}}}